If I was going to provide world-facing services, I'd definitely want to go with a rented server (physical or virtual) with a high bandwidth connection.

If I'm just providing services to friends and family, running something out of my house would be worth considering.

One service I forgot to mention is a backup service. For that you'd definitely want to be located somewhere else than the same building with your computer. I currently just use Apple's Time Machine. It's very convenient and works great, but my disk is sitting about two inches from my desktop machine—much too vulnerable to a common disaster.